Data Mining for Education Ryan S.J.d. Baker, Carnegie Mellon University, Pittsburgh, Pennsylvania, USA rsbaker@cmu.edu Article to appear as Baker, R.S.J.d. (in press) Data Mining for Education. To appear in McGaw, B., Peterson, P., Baker, E. (Eds.) International Encyclopedia of Education (3rd edition). Oxford, UK: Elsevier. This is a pre-print draft. Final article may involve minor changes and different formatting.

1. Data Mining for Education
Ryan S.J.d. Baker, Carnegie Mellon University, Pittsburgh, Pennsylvania, USA
rsbaker@cmu.edu
Article to appear as
Baker, R.S.J.d. (in press) Data Mining for Education. To appear in McGaw, B., Peterson, P.,
Baker, E. (Eds.) International Encyclopedia of Education (3rd edition). Oxford, UK: Elsevier.
This is a pre-print draft. Final article may involve minor changes and different formatting.
I would like to thank Cristobal Romero, Sandip Sinharay, and Joseph Beck for their comments
and suggestions on this document, and Joseph Beck and Jack Mostow for their permission to
discuss their research as a “best practices” case study in this article.

2. Data Mining for Education
Ryan S.J.d. Baker, Carnegie Mellon University, Pittsburgh, Pennsylvania, USA
Introduction
Data mining, also called Knowledge Discovery in Databases (KDD), is the field of discovering
novel and potentially useful information from large amounts of data. Data mining has been
applied in a great number of fields, including retail sales, bioinformatics, and counter-terrorism.
In recent years, there has been increasing interest in the use of data mining to investigate
scientific questions within educational research, an area of inquiry termed educational data
mining. Educational data mining (also referred to as “EDM”) is defined as the area of scientific
inquiry centered around the development of methods for making discoveries within the unique
kinds of data that come from educational settings, and using those methods to better understand
students and the settings which they learn in.
Educational data mining methods often differ from methods from the broader data mining
literature, in explicitly exploiting the multiple levels of meaningful hierarchy in educational data.
Methods from the psychometrics literature are often integrated with methods from the machine
learning and data mining literatures to achieve this goal.
For example, in mining data about how students choose to use educational software, it may be
worthwhile to simultaneously consider data at the keystroke level, answer level, session level,
student level, classroom level, and school level. Issues of time, sequence, and context also play
important roles in the study of educational data.
Educational data mining has emerged as an independent research area in recent years,
culminating in 2008 with the establishment of the annual International Conference on
Educational Data Mining, and the Journal of Educational Data Mining.
Advantages Relative to Traditional Educational Research Paradigms
Educational data mining offers several advantages, vis-à-vis more traditional educational
research paradigms, such as laboratory experiments, in-vivo experiments, and design research.
In particular, the advent of public educational data repositories such as the PSLC DataShop and
the National Center for Education Statistics (NCES) data sets has created a base which makes
educational data mining highly feasible. In particular, the data from these repositories is often
both ecologically valid (inasmuch as it is data about the performance and learning of genuine
students, in genuine educational settings, involved in authentic learning tasks), and increasingly

3. easy to rapidly access and begin research with. Balancing feasibility with ecological validity is
often a difficult challenge for researchers in other educational research paradigms. By contrast,
researchers who use data from these repositories can dispense with traditionally time-consuming
steps such as subject recruitment (e.g. recruitment of schools, teachers, and students), scheduling
of studies, and data entry (since data is already online). While the use of previously collected
data has the potential to limit analyses to questions involving the types of data collected, in
practice data from repositories or prior research has been useful for analyzing research questions
far outside the purview of what the data were originally intended to study, particularly given the
advent of models that can infer student attributes (such as strategic behavior and motivation)
from the type of data in these repositories.
This increase in speed and feasibility has had the benefit of making replication much more
feasible. Once a construct of educational interest (such as off-task behavior, or whether or not a
skill is known) has been empirically defined in data, it can be transferred to new data sets. The
transfer of constructs is not trivial – often, the same construct can be subtly different at the data
level, within data from a different context or system – but transfer learning and rapid labeling
methods have been successful in speeding up the process of developing or validating a model for
a new context. This has led to many educational data mining analyses being replicated across
data from several learning systems or contexts.
Increasingly, the existence of data from thousands of students, having broadly similar learning
experiences (such as using the same learning software), but in very different contexts, gives
leverage that was never before possible, for studying the influence of contextual factors on
learning and learners. It has historically been difficult to study how much the differences
between teachers and classroom cohorts influence specific aspects of the learning experience;
this sort of analysis becomes much easier with educational data mining. Similarly, the concrete
impacts of fairly rare individual differences have been difficult to statistically study with
traditional methods (leading case studies to be a dominant research method in this area) –
educational data mining has the potential to extend a much wider tool set to the analysis of
important questions in individual differences.
Main Approaches
<put Table 1 here>
There are a wide variety of current methods popular within educational data mining. These
methods fall into the following general categories: prediction, clustering, relationship mining,
discovery with models, and distillation of data for human judgment. The first three categories are
largely acknowledged to be universal across types of data mining (albeit in some cases with
different names). The fourth and fifth categories achieve particular prominence within
educational data mining.

4. Prediction
In prediction, the goal is to develop a model which can infer a single aspect of the data (predicted
variable) from some combination of other aspects of the data (predictor variables). Prediction
requires having labels for the output variable for a limited data set, where a label represents some
trusted “ground truth” information about the output variable’s value in specific cases. In some
cases, however, it is important to consider the degree to which these labels may in fact be
approximate, or incompletely reliable.
Prediction has two key uses within educational data mining. In some cases, prediction methods
can be used to study what features of a model are important for prediction, giving information
about the underlying construct. This is a common approach in programs of research that attempt
to predict student educational outcomes (cf. Romero et al, 2008) without predicting intermediate
or mediating factors first. In a second type of usage, prediction methods are used in order to
predict what the output value would be in contexts where it is not desirable to directly obtain a
label for that construct (for example, in previously collected repository data, where desired
labeled data may not be available, or in contexts where obtaining labels could change the
behavior being labeled, such as modeling affective states, where self-report, video, and
observational methods all present risks of altering the construct being studied).
For example, consider research attempting to study the relationship between learning and gaming
the system, attempting to succeed in an interactive learning environment by exploiting properties
of the system rather than by learning the material. If a researcher has the goal of studying this
construct across a full year of software usage within multiple schools, it may not be tractable to
directly assess, using non data-mining methods, whether each student is gaming, at each point in
time. Baker et al (2008) developed a prediction model by using observational methods to label a
small data set, developing a prediction model using automatically collected data from
interactions between students and the software for predictor variables, and then validating the
model’s accuracy when generalized to additional students and contexts. They were then able to
study their research question in the context of the full data set.
Broadly, there are three types of prediction: classification, regression, and density estimation. In
classification, the predicted variable is a binary or categorical variable. Some popular
classification methods include decision trees, logistic regression (for binary predictions), and
support vector machines. In regression, the predicted variable is a continuous variable. Some
popular regression methods within educational data mining include linear regression, neural
networks, and support vector machine regression. In density estimation, the predicted variable is
a probability density function. Density estimators can be based on a variety of kernel functions,
including Gaussian functions. For each type of prediction, the input variables can be either

5. categorical or continuous; different prediction methods are more effective, depending on the type
of input variables used.
Popular methods for assessing the goodness of a predictor include linear correlation, Cohen’s
Kappa, and A’ (the area under the receiver-operating curve – e.g. Bradley, 2007). Percent
accuracy is generally not preferred for classification, as values of accuracy are highly dependent
on the base rates of different classes (and hence, a very high accuracy can in some cases be
achieved by a classifier that simply always predicts the majority class). When computing the
goodness of a predictor, it is important to account for non-independence of different observations
involving the same student – to achieve this goal, educational data mining researchers often
apply meta-analytical methods that can account for partial non-independence, such as Strube’s
(1985) Adjusted Z, or select overly conservative estimators that assume complete non-
independence.
Clustering
In clustering, the goal is to find data points that naturally group together, splitting the full data set
into a set of clusters. Clustering is particularly useful in cases where the most common categories
within the data set are not known in advance. If a set of clusters is optimal, within a category,
each data point will in general be more similar to the other data points in that cluster than data
points in other clusters. Clusters can be created at several different possible grain-sizes: for
example, schools could be clustered together (to investigate similarities and differences between
schools), students could be clustered together (to investigate similarities and differences between
students), or student actions could be clustered together (to investigate patterns of behavior) (cf.
Amershi & Conati, 2006; Beal, Qu, & Lee, 2006).
Clustering algorithms can either start with no prior hypotheses about clusters in the data (such as
the k-means algorithm with randomized restart), or start from a specific hypothesis, possibly
generated in prior research with a different data set (using the Expectation Maximization
algorithm to iterate towards a cluster hypothesis for the new data set). A clustering algorithm can
postulate that each data point must belong to exactly one cluster (such as in the k-means
algorithm), or can postulate that some points may belong to more than one cluster or to no
clusters (such as in Gaussian Mixture Models).
The goodness of a set of clusters is usually assessed with reference to how well the set of clusters
fits the data, relative to how much fit might be expected solely by chance given the number of
clusters, using statistical metrics such as the Bayesian Information Criterion.
Relationship Mining

6. In relationship mining, the goal is to discover relationships between variables, in a data set with a
large number of variables. This may take the form of attempting to find out which variables are
most strongly associated with a single variable of particular interest, or may take the form of
attempting to discover which relationships between any two variables are strongest.
Broadly, there are four types of relationship mining: association rule mining, correlation mining,
sequential pattern mining, and causal data mining. In association rule mining, the goal is to find
if-then rules of the form that if some set of variable values is found, another variable will
generally have a specific value. For example, a rule might be found of the form {student is
frustrated, student has stronger goal of learning than goal of performance} {student frequently
asks for help}. In correlation mining, the goal is to find (positive or negative) linear correlations
between variables. In sequential pattern mining, the goal is to find temporal associations between
events – for example, to determine what path of student behaviors leads to an eventual learning
event of interest. In causal data mining, the goal is to find whether one event (or observed
construct) was the cause of another event (or observed construct), either by analyzing the
covariance of the two events (e.g. TETRAD – Scheines et al, 1994) or by using information
about how one of the events was triggered. For example, if a pedagogical event is randomly
chosen using automated experimentation (Mostow, 2008), and frequently leads to a positive
learning outcome, a causal relationship can be inferred.
Relationships found through relationship mining must satisfy two criteria: statistical significance,
and interestingness. Statistical significance is generally assessed through standard statistical tests,
such as F-tests. Because large numbers of tests are conducted, it is necessary to control for
finding relationships through chance. One method for doing this is to use post-hoc statistical
methods or adjustments which control for the number of tests conducted, such as the Bonferroni
adjustment. This method can increase confidence that an individual relationship found was not
likely to be due to chance. An alternate method is to assess the overall probability of the pattern
of results found, using Monte Carlo methods. This method assesses how likely it is that the
overall pattern of results arose due to chance.
The interestingness of each finding is assessed in order to reduce the set of rules/ correlations/
causal relationships communicated to the data miner. In very large data sets, hundreds of
thousands of significant relationships may be found. Interestingness measures attempt to
determine which findings are the most distinctive and well-supported by the data, in some cases
also attempting to prune overly similar findings. There are a wide variety of interestingness
measures, including support, confidence, conviction, lift, leverage, coverage, correlation, and
cosine. Some investigations have suggested that lift and cosine may be particularly relevant
within educational data (Merceron & Yacef, 2008).
Discovery with Models

7. In discovery with a model, a model of a phenomenon is developed via prediction, clustering, or
in some cases knowledge engineering (within knowledge engineering, the model is developed
using human reasoning rather than automated methods). This model is then used as a component
in another analysis, such as prediction or relationship mining.
In the prediction case, the created model’s predictions are used as predictor variables in
predicting a new variable. For instance, analyses of complex constructs such as gaming the
system within online learning have generally depended on assessments of the probability that the
student knows the current knowledge component being learned (Baker et al, 2008; Walonoski &
Heffernan, 2006). These assessments of student knowledge have in turn depended on models of
the knowledge components in a domain, generally expressed as a mapping between exercises
within the learning software and knowledge components.
In the relationship mining case, the relationships between the created model’s predictions and
additional variables are studied. This can enable a researcher to study the relationship between a
complex latent construct and a wide variety of observable constructs.
Often, discovery with models leverages the validated generalization of a prediction model across
contexts. For instance, Baker (2007) used predictions of gaming the system across a full year of
educational software data to study whether state or trait factors were better predictors of how
much a student would game the system. Generalization in this fashion relies upon appropriate
validation that the model accurately generalizes across contexts.
Distillation of Data for Human Judgment
Another area of interest within educational data mining is the distillation of data for human
judgment. In some cases, human beings can make inferences about data, when it is presented
appropriately, that are beyond the immediate scope of fully automated data mining methods. The
methods in this area of educational data mining are information visualization methods –
however, the visualizations most commonly used within EDM are often different than those most
often used for other information visualization problems (cf. Kay et al, 2006; Hershkovitz &
Nachmias, 2008), owing to the specific structure, and the meaning embedded within that
structure, often present in educational data.
Data is distilled for human judgment in educational data mining for two key purposes:
identification and classification. When data is distilled for identification, data is displayed in
ways that enable a human being to easily identify well-known patterns that are nonetheless
difficult to formally express. For example, one classic educational data mining visualization is
the learning curve, which displays the number of opportunities to practice a skill on the X axis,

8. and displays performance (such as percent correct or time taken to respond) on the Y axis. A
curve with a smooth downward progression that is steep at first and gentler later indicates a well-
specified knowledge component model. A sudden spike upwards, by contrast, indicates that
more than one knowledge component is included in the model (cf. Corbett & Anderson, 1995).
Alternately, data may be distilled for human labeling, to support the later development of a
prediction model. In this case, sub-sections of a data set are displayed in visual or text format,
and labeled by human coders. These labels are then generally used as the basis for the
development of a predictor. This approach has been shown to speed the development of
prediction models of complex phenomena such as gaming the system by around 40 times,
relative to prior approaches for collecting the necessary data (Baker & de Carvalho, 2008).
Main Applications
There have been a wide number of applications of educational data mining, as reflected
throughout this chapter. In this section, four areas of application that have received particular
attention within the field are discussed.
One key area of application is in improving student models, models that provide detailed
information about a student’s characteristics or states, such as knowledge, motivation, meta-
cognition, and attitudes. Modeling the individual differences between students, in order to enable
software to respond to those individual differences, is a key theme in educational software
research. In the last few years educational data mining methods have enabled considerable
expansion in the sophistication of student models. In particular, educational data mining methods
have enabled researchers to make higher-level inferences about students’ behavior, such as when
a student is gaming the system, when a student has “slipped” (making an error despite knowing a
skill), and when a student is engaging in self-explanation (cf. Shih, Koedinger, & Scheines,
2008). These richer student models have been useful in two fashions. First, these models have
increased our ability to predict student knowledge and future performance – incorporating
models of guessing and slipping into predictions of student future performance has increased the
accuracy of these predictions by up to 48% (Baker, Corbett, & Aleven, 2008). Second, these
models have enabled researchers to study what factors lead students to make specific choices in a
learning setting, a type of scientific discovery with models discussed below.
A second key area of application is in discovering or improving models of the knowledge
structure of the domain. In educational data mining, methods have been created for rapidly
discovering accurate domain models directly from data. These methods have generally combined
psychometric modeling frameworks with advanced space-searching algorithms, and are
generally posed as prediction problems for the purpose of model discovery (for example,
attempting to predict whether individual actions will be correct or incorrect, using different

9. domain models, is one common method for developing these models). Barnes, Bitzer, & Vouk
(2005) have proposed algorithms for automatically discovering a Q-Matrix from data. Cen,
Koedinger, & Junker (2006) proposed algorithms for using codified expert knowledge about
differences between items to drive automated search for IRT models. Pavlik et al (2008) has
proposed algorithms for finding partial order knowledge structure models (cf. Desmarais, Maluf,
& Liu, 1996), by looking at the covariation of individual items.
A third key area of application is in studying the pedagogical support provided by learning
software. Modern educational software gives a variety of types of pedagogical support to
students. Discovering which pedagogical support is most effective has been a key area of interest
for educational data miners. Learning decomposition (Beck & Mostow, 2008), a type of
relationship mining, fits exponential learning curves to performance data, relating student
success to the amount of each type of pedagogical support a student has received (with a weight
for each type of support). The weights indicate how effective each type of pedagogical support is
for improving learning. An illustrative example is given in the next section.
A fourth key area of application of educational data mining is for scientific discovery about
learning and learners. This takes on several forms. Applying educational data mining to answer
questions in any of the three areas previously discussed (e.g. student models, domain models,
and pedagogical support) can have broader scientific benefits; for example, the study of
pedagogical support may have the long-term potential to enrich theories of scaffolding. Beyond
just these three areas, however, there have been many analyses aimed directly towards scientific
discovery. Discovery with models is a key method for scientific discovery via educational data
mining. Research on studying whether state or trait factors were better predictors of how much a
student would game the system (Baker, 2007) is a prominent example of this approach within
educational data mining research. Learning decomposition methods are another prominent
method for conducting scientific discovery about learning and learners.
Illustrative Example
In this section, a brief case study is discussed, as a concrete “best practices” example of how the
educational data mining method of learning decomposition (a type of relationship mining) was
used to determine the relative efficacy of different types of learning material presented to
students.
In Beck and Mostow (2008), data was obtained from 346 American elementary school students
reading 6.9 million words, over the course of a year, while using intelligent tutor software that
teaches reading. These words were presented in the form of stories, and students and the
software took turns choosing stories (the software’s choice of stories was based on the student’s
approximate grade reading level). Beck and Mostow were interested in determining whether re-

10. reading a story (a popular option for children) is more or less effective at promoting word
learning than encountering the same word in a different story. They were also interested in
whether there would be individual differences, such that some students would benefit from a
different pattern of practice than others.
Beck and Mostow obtained data for each student’s performance in reading each story within the
software. Reading time was used as a continuous measure of word knowledge; mis-reading and
help-requests were also taken into account, reading opportunities where these behaviors occurred
were assigned a time of 3.0 seconds (99.9% of word reads were faster than 3.0 seconds). An
exponential model of practice was set up, relating response time to the function:
‫݁݉݅ݐ‬ ൌ ‫ܣ‬ ‫כ‬ ݁ି௕ ሺௐ‫כ‬௧భା௧మሻ
.
In this equation, parameter A represents student performance on the first opportunity to read a
given word, parameter b represents the overall speed of learning, e is 2.718, and t1 and t2
represent the number of times the word is read, within two different types of practice. In this
case, t1 was defined as the number of times the word was read when re-reading a story and t2
was defined as the number of times the word was read when reading a story for the first time. W
is the relative speed gain associated with the two types of practice. If W equals 1, the two types
of practice are considered to be equally effective; if W is above 1, opportunities of type t1 are
more effective than opportunities of type t2 (and the reverse holds true if W is below 1).
Across the population of students, the median value of W for re-reading obtained by Beck and
Mostow was 0.49, suggesting that re-reading a story leads to approximately half as much
learning as reading a new story. 95 of the 346 students had a W parameter statistically
significantly under 1, whereas only 7 students had a W parameter value statistically significantly
over 1, a statistically significant result across the entire class.
Beck and Mostow next used the values of W from the model in a subsequent logistic regression
analysis (an example of discovery with models). In this analysis, the learning decomposition
model was used to split the population into students who benefitted from re-reading and students
who did not benefit from re-reading, and a variety of explanatory variables were tested to see if
they explained which students benefitted from re-reading. This analysis determined that students
with overall low reading speed who were receiving special needs learning support actually
benefitted from re-reading.
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Further Reading
Moore, A. (2005) Statistical Data Mining Tutorials. Available online at
http://www.autonlab.org/tutorials/ . Retrieved June 27, 2008.
Baker, R.S.J.d., Barnes, T., Beck, J.E. (Eds.) (2008) Proceedings of the 1st
International
Conference on Educational Data Mining.
Baker, R.S.J.d., Beck, J.E., Berendt, B., Kroner, A., Menasalvas, E., Weibelzahl, S. (2007)
Complete On-Line Proceedings of the Workshop on Data Mining for User Modeling, at the 11th
International Conference on User Modeling (UM 2007).
Heiner, C., Heffernan, N.T., Barnes, T., (Eds.) (2007) Proceedings of the Workshop on
Educational Data Mining, at the 13th
International Conference on Artificial Intelligence in
Education.
Romero, C., Ventura, S. (2006) Data Mining in e-Learning. Southampton, UK: WIT Press.
Romero, C., Ventura, S. (2007) Educational Data Mining: A Survey from 1995 to 2005. Expert
Systems with Applications, 33(1), 135-146.
Witten, I.H., Frank, E. (2005) Data Mining: Practical Machine Learning Tools and Techniques:
2nd
Edition. San Francisco: Morgan Kaufmann.
Tables/Illustrations
Category of Method Goal of Method Key applications
Prediction Develop a model which can
infer a single aspect of the
data (predicted variable) from
some combination of other
aspects of the data (predictor
variables)
Detecting student behaviors
(e.g. gaming the system, off-
task behavior, slipping);
Developing domain models;
Predicting and understanding
student educational outcomes
Clustering Find data points that naturally
group together, splitting the
Discovery of new student
behavior patterns;

14. full data set into a set of
categories
Investigating similarities and
differences between schools
Relationship Mining Discover relationships
between variables
Discovery of curricular
associations in course
sequences; Discovering which
pedagogical strategies lead to
more effective/robust learning
Discovery with Models A model of a phenomenon
developed with prediction,
clustering, or knowledge
engineering, is used as a
component in further
prediction or relationship
mining.
Discovery of relationships
between student behaviors,
and student characteristics or
contextual variables; Analysis
of research question across
wide variety of contexts
Distillation of Data for Human
Judgment
Data is distilled to enable a
human to quickly identify or
classify features of the data.
Human identification of
patterns in student learning,
behavior, or collaboration;
Labeling data for use in later
development of prediction
model
Table 1: The primary categories of educational data mining